Can X-Ray Observations Improve Optical-UV-based Accretion-rate Estimates for Quasars?

Current estimates of the normalized accretion rates of quasars (L/L _Edd) rely on measuring the velocity widths of broad optical-UV emission lines (e.g., Hβ and Mg II λ2800). However, such lines tend to be weak or inaccessible in the most distant quasars, leading to increasing uncertainty in L/L _Edd estimates at z > 6. Utilizing a carefully selected sample of 53 radio-quiet quasars that have Hβ and C IV λ1549 spectroscopy as well as Chandra coverage, we searched for a robust accretion-rate indicator for quasars, particularly at the highest-accessible redshifts (z ~ 6-7). Our analysis explored relationships between the Hβ-based L/L _Edd, the equivalent width (EW) of C IV, and the optical-to-X-ray spectral slope (α _ox). Our results show that EW(C IV) is the strongest indicator of the Hβ-based L/L _Edd parameter, consistent with previous studies, although significant scatter persists particularly for sources with weak C IV lines. We do not find evidence for the α _ox parameter improving this relation, and we do not find a significant correlation between α _ox and Hβ-based L/L _Edd. This absence of an improved relationship may reveal a limitation of our sample. X-ray observations of additional luminous sources, found at z ≳ 1, may allow us to mitigate the biases inherent in our archival sample and test whether X-ray data could improve L/L _Edd estimates. Furthermore, deeper X-ray observations of our sources may provide accurate measurements of the hard-X-ray power-law photon index (Γ), which is considered an unbiased L/L _Edd indicator. Correlations between EW(C IV) and α _ox with a Γ-based L/L _Edd may yield a more robust prediction of a quasar normalized accretion rate.